"I've stepped to one side, but I'm going to think about it," Sabella told Ole. No-one at Estudiantes was available to comment.
Former midfielder Sabella, who steered the club to their fourth South American Libertadores Cup in 2009 and this season's Apertura title in December, said he would decide on Thursday if he was going ahead with his plan to quit the club.
He told Ole players and directors had tried to persuade him to stay "so I told them I would take time until tomorrow to give them my reply."
Dozens of fans turned up at Estudiantes' training complex in a La Plata city suburb to try to persuade Sabella to stay.
Media said he was unhappy with the club's lack of response to his request for another defender and striker to strengthen a squad facing the double challenge of defending their Argentine title and playing the Libertadores Cup.
Estudiantes, captained by Juan Sebastian Veron whom the club hope will persuade Sabella to stay, are at home to Newell's Old Boys on February 11 in their opening Clausura match.
The day had begun badly for Estudiantes when goalkeeper Agustin Orion was mugged on his way to training. He had his car stolen and was left by the side of the motorway.
"They put a revolver against my chest, it was very nasty," Orion was quoted as saying by Ole.
